1440edo: Difference between revisions
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1440edo is in[[consistent]] to the [[5-odd-limit]] and does poorly with approximating lower harmonics. However, 1440edo is worth considering as a higher-limit system, where it has excellent representation of the 2.27.15.21.33.17.19.23.31 [[subgroup]]. It may also be considered as every third step of [[4320edo]] in this regard. | 1440edo is in[[consistent]] to the [[5-odd-limit]] and does poorly with approximating lower harmonics. However, 1440edo is worth considering as a higher-limit system, where it has excellent representation of the 2.27.15.21.33.17.19.23.31 [[subgroup]]. It may also be considered as every third step of [[4320edo]] in this regard. | ||
Latest revision as of 05:48, 21 February 2025
| ← 1439edo | 1440edo | 1441edo → |
1440 equal divisions of the octave (abbreviated 1440edo or 1440ed2), also called 1440-tone equal temperament (1440tet) or 1440 equal temperament (1440et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1440 equal parts of about 0.833 ¢ each. Each step represents a frequency ratio of 21/1440, or the 1440th root of 2.
1440edo is inconsistent to the 5-odd-limit and does poorly with approximating lower harmonics. However, 1440edo is worth considering as a higher-limit system, where it has excellent representation of the 2.27.15.21.33.17.19.23.31 subgroup. It may also be considered as every third step of 4320edo in this regard.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.288 | +0.353 | +0.341 | +0.257 | +0.349 | +0.306 | +0.065 | +0.045 | -0.013 | +0.052 | +0.059 |
| Relative (%) | -34.6 | +42.4 | +40.9 | +30.8 | +41.8 | +36.7 | +7.8 | +5.4 | -1.6 | +6.3 | +7.1 | |
| Steps (reduced) |
2282 (842) |
3344 (464) |
4043 (1163) |
4565 (245) |
4982 (662) |
5329 (1009) |
5626 (1306) |
5886 (126) |
6117 (357) |
6325 (565) |
6514 (754) | |
Subsets and supersets
Since 1440 factors into 25 × 32 × 5, 1440edo is notable for having a lot of subset edos, the nontrivial ones being 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 72, 80, 90, 96, 120, 144, 160, 180, 240, 288, 360, 480, and 720. It is also a highly factorable equal division.
As an interval size measure, one step of 1440edo is called decifarab.